Method and apparatus for charge distribution analysis

ABSTRACT

Method and apparatus of charge distribution analysis insulating and semiconducting dielectric materials to measure by using a Coulomb Balance surface/subsurface space charge layers and the sign, mobility and polarizability of charge carriers. The technique includes measuring the force, attractive or repellent, between a bias electrode to which a voltage is applied and a dielectric material in a condensor half cell arrangement. An apparatus is provided for heating a sample for causing the generation of surface/subsurface charges, and then for applying an external potential while the sample is maintained at a high temperature. The effective mass of the sample is detected by determining the amount of force necessary to restore a balance arm, by which the sample is supported, to its original position, the alteration in position being due to attractive or repulsive electrostatic forces between the sample and the electrodes. The effective mass reflects the amount of peroxies or impurities within the sample, and the method and apparatus may be used for scientific mineral composition analysis, quality control of the purity of semiconductors, and in other applications. The heating of the sample may by a combination of any of conductive, convective and radiative means. In a preferred embodiment, the sample is supported on a vertically-disposed beam.

This application is a continuation of application Ser. No. 07/499,323,filed Nov. 28, 1989, now abandoned.

BACKGROUND OF THE INVENTION

The present invention is directed to a new apparatus and method ofcharge distribution analysis, or CDA, to measure surface and/orsubsurface charge layers, the sign of dominant charge carriers, andtheir mobility in--as well as the dielectric constant of--insulating andsemiconducting dielectric materials.

The existence of surface/subsurface charge layers has been theoreticallypredicted on the basis of fundamental thermodynamic laws, specificallyfor ionic insulators. For instance, discussions of such charge layersmay be found in the following articles: K. Lehovec, J. Chem. Phys. 21,1123 (1953); K. L. Kliewer and J. S. Koehler, Phys. Rev. 140A, 1226(1965); and W. D. Kingery, J .Am. Ceram. Soc. 57, 1 (1974) and 57, 74(1974). A discussion of oxide insulators with electronic defects isfound in the article by B. V. King and F. Freund, Phys. Rev B29, 5814(1984). The presence of such charge layers has been concluded from avariety of indirect observations such as the preferred segregation ofcertain aliovalent cations to surfaces and/or grain boundaries (Kingery1974 articles cited above), the deflection of low energy electron or ionbeams from surfaces, the energy dispersion of photoelectrons emittedfrom surfaces and many manifestations of electrostatic adhesion. Each ofthe above references is hereby incorporated herein by reference.

However, no method has existed until now for directly measuring andquantifying surface/subsurface charge layers, and for determining thesign and mobility of the dominant charge carriers.

Prior methods such as the measurement of cation surface or grainboundary segregation in ceramics are indirect and limited to hightemperatures. They require thermal pretreatment of the samples,extensive sample preparation for observation of frozen-in disequilibriumstates by microanalytical techniques (Kingery 1974) or extremely cleansurface conditions in ultrahigh vacuum. Prior methods such as thedeflection or energy dispersion of low energy charged beams, bothelectrons and other particles, inherently require high or ultrahighvacua, and are restricted to very thin surface/subsurface layers due tothe limited depth of penetration or escape depth of low energy electronor ion beams.

Prior methods such as based on electrostatic adhesion are qualitative atbest, giving no or very limited information about the strength of theeffect, about the concentration and the nature of the dominant chargecarriers.

SUMMARY OF THE INVENTION

It is an object of this invention to provide a method for chargedistribution analysis, or CDA, for measuring surface/subsurface chargelayers, and for determining the sign of the dominant charge carriers andtheir mobility in insulating and semiconducting dielectric materials.

It is a further object of this invention to utilize as a force sensor anelectronic force-sensitive device or a balance, appropriately called aCoulomb Balance, to measure the force between a dielectric materialcarrying a surface/subsurface charge layer and a bias electrode at closeproximity to which a voltage may be applied.

It is still another object of this invention to measure this force as afunction of various physical parameters including, but not limited to,the sign of the applied voltage, the magnitude of the applied voltage,sample position, sample temperature, photon flux, phonon (sound wave)flux, electron bombardment and particle bombardment.

It is a further object of this invention to provide a method formeasuring the magnetic susceptibilities of materials independent of masslosses or mass gains of these materials during measurement.

It is a further object of this invention to provide a method formeasuring simultaneously, within the same apparatus, dielectric andmagnetic susceptibilities and derivative properties of materialsindependent of mass losses or mass gains during measurement.

It is a further object of this invention to utilize a vertical pendulumwith its axis z set parallel to the prevailing gravitational vector g,with forcesensitive devices or transmittors attached to the pendulum tomeasure forces acting in the xy plane perpendicular to the g vector.

It is an additional object of this invention to utilize for themeasurement of the said forces a vertical pendulum with the sampleloaded below the center of gravity.

It is an additional object of this invention to utilize for themeasurement of the said forces a vertical pendulum with the sampleloaded above the center of gravity.

It is yet another object of this invention to measure the said force ina static mode.

It is yet another object of this invention to measure the said force ina dynamic mode.

It is an additional object of this invention to utilize for themeasurement of said force a horizontal beam balance with top-loading ordirect loading on the beam.

It is a further object of this invention to utilize for the measurementof said force a horizontal beam balance with bottom-loading via ahang-down wire.

It is also an object of this invention to utilize for the measurement ofsaid force a torsion balance.

It is an additional object of this invention to utilize for themeasurement of said force an electronic force-sensitive device includingbut not limited to position-sensitive or pressure-sensitive ortension-sensitive devices.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a charge distribution analysis apparatus according to thepresent invention.

FIG. 2A and 2B show responses to applied electric fields of,respectively, an ideal dielectric material and a dielectric materialwith charge carriers of a certain mobility.

FIGS. 3A-3D show force measurements due to charge mobility for fourlimiting cases of charge distribution.

FIG. 4 shows an apparatus according to the present invention.

FIG. 4A shows an enlarged view, partially cut away, of a portion of anapparatus according to the invention.

FIG. 5 shows an enlarged view of a portion of a device according to thepresent invention.

FIG. 6 shows a portion of an alternative embodiment of the presentinvention.

FIGS. 7-13 show various test results utilizing the method and apparatusof the present invention.

FIGS. 14-18 show alternative embodiments of the invention with avertically-disposed beam.

DETAILED DESCRIPTION OF THE INVENTION

Turning now to the drawings, more particularly to FIG. 1, there isshown, in accordance with the invention, an example of a Coulomb Balancefor charge distribution analysis using a conventional bottom-loadingbalance 10, such as the TGS Thermobalance produced by Perkin-Elmer,which is marked with U.S. Pat. No. 3,140,097, which is incorporatedherein by reference. In the present invention, a hang-down wire 20 isutilized in conjunction with the balance 10, and a bias electrode 30 isalso used, to which a positive or negative voltage can be applied. Agrounded furnace 40 is used to vary the temperature of the sample 50.The sample 50 preferably has a flat, polished surface 60, and issuspended in such a manner as to be fully insulated from ground. Thewire 20 may be of silicon dioxide (SiO₂) In the preferred embodiment,the electrode 30 is of nickel.

As shown in FIG. 5, the electrode 30 preferably has a flat portion 70which is substantially parallel to the flat surface 60 and is positioneda predetermined distance above the sample 50.

The electrode/sample arrangement to be used in CDA and exemplified inthe insert in FIG. 1 is that of a capacitor half cell where the sampleis placed in an nonhomogeneous electric field. The bias electrode 30forms one electrode of a capacitor, and is carried by an insulatedsupport 100. As shown schematically in FIGS. 1 and 4, the electrode 30is connected to an electrical biasing circuit.

The furnace 40 is preferably formed from ceramic, and has windings 80embedded therein, with the windings 80 defining the counterelectrode forthe capacitor 90. Thus, the sample 50, being positioned between theelectrode 30 and the windings 80, acts as a dielectric for the capacitor90. The windings 80 are typically of platinum.

Other forms of electrodes than shown as the example in FIGS. 1 and 5 maybe used in accordance with the invention, including but not limited towedge-shaped or needle-shaped electrodes or 1-dimensional or2-dimensional electrode arrays, and other types of force-measuringdevices. Also other force measuring devices than the balance shown as anexample in FIG. 1 may be used in accordance with the invention allowingto arrange the bias electrode differently, to substitute the furnace byor to combine it with a cooling jacket, or to replace it by aradiation-heating device and to add access ports or openings foradditional instrumentation.

Both the sample 50 and the electrode-bearing device, while being atground potential or any chosen positive or negative potential, beelectrically as highly insulated as possible.

The gap or distance 110 (shown in FIG. 5) between the sample 50 and thebias electrode 30 to which a positive or negative potential may beapplied, is preferably smaller than the distance to any equipotentialsurface by which a counterelectrode may be defined. In addition, the gap110 should be smaller than, or of the same order of magnitude as, thethickness of the sample measured in the direction of the electric fieldlines, such as field lines 120 shown in FIG. 5. In the configuration ofFIG. 5, this means that the gap should be less than approximately thethickness of the sample 50 measured in the vertical direction from thepoint of view of that Figure.

The following discussion is of a theory which applicants believe explainthe operation of the present invention. Following the theoreticaldiscussion is the discussion of the actual operation of the inventionand its method of use.

THEORY

Evaluating the Maxwell equations one can deduce the force F acting on adielectric in an electric external field E₀ :

    F=-∫.sub.v (P·grad)E.sub.0 dV                (1)

where P is the polarization of the dielectric and E₀ is the externalapplied field in the absence of the dielectric. The integral is to betaken over some volume fully enclosing the dielectric body, but withoutthe sources of the field. If the medium is an ideal dielectric, therelation ##EQU1## holds. Inserting this into equation 1 and using thefact that ∇·E₀ =0 we find: ##EQU2## Since the electric field E₀ isproportional to the potential difference U of the electrodes, F˜U² orU˜√|F|, the slope of U versus √|F | is proportional to √ε-1.

From equation 2 we also see that F vanishes in a constant electricfield. To exert a force on the dielectric an nonhomogeneous electricfield is therefore essential. At the same time a change in the polarityof E₀ should leave F invariant, which is not observed experimentally. Itmay also be noted that the strikingly different behavior the √F vs·μcurve under positive and negative bias cannot be due to temperaturegradients, since when evaluating the force F one finds a term F_(T)˜E_(o) ² grad T. Since this term is quadratic in E₀, it is invariantunder changes of the polarity of E₀.

In order to explain the behavior of the dielectric in an nonhomogeneouselectric field we must assume additional second order terms in P whichmay be of the form: ##EQU3## In principle both the applied externalfield E₀ and P can be calculated:

The applied external electric field is given by E₀ =-grad φ₀, where φ₀is the scalar potential. φ₀ depends only the geometry of the conductorsand must be a solution of the Laplace equation Δφ₀ =0 using appropriateboundary conditions. In order to calculate P we first note that theelectric induction D is defined by D=E+4πP. P satisfies Maxwell'sequation div P=-p, where p is the induced volume charge. The totalcharge in the body vanishes, ∫pdV=0, but note that ∫prdV=∫PdV is thetotal dipole moment of the dielectric body. After making a microscopicmodel of P, the dielectric constant and the scalar potential φ₀,mustsatisfy a set of two equations:

a) αφ=0 and

b) grad □ grad φ=0, where we have used that E=-grad φ anddivD=divεE=-div(ε grad φ)=0. If the dielectric body is homogeneous, gradε=0 which reduces the problem to solving Δφ=0.

With a known geometry, the dielectric constant ε of the sample may bedetermined as follows. (Note that in the following discussion, thepolarization P is defined slightly differently, so as to include thefour contributors P1, P2, P3 and P4.)

When a dielectric material is placed in an external electric field offield strength E_(ext), it becomes polarized and its polarization P isgiven by: ##EQU4## where ε₀ is the permittivity of vacuum, ε is thedielectric constant and (ε-1) the dielectric susceptibility χ_(diel). Pcontains at least four contributions, P=P1+P2+P3+P4, which denote,respectively, (1) those from the ideal dielectric due to the deformationof electron clouds and the relative displacements of nuclei, (2) thosefrom local dipoles which may rotate but not diffuse, (3) those frommobile charges which can diffuse over macroscopic distances, and (4)those from surface charges.

By placing a dielectric in a static inhomogeneous electric field (with afield gradient along the z direction) we generate a force F_(z) whichcauses an attraction towards the region of higher electric fielddensity. The force F_(z).sup.± =F_(z) (±E_(ext)) can be calculated byevaluating the Maxwell equations:

    F.sub.x.sup.± =-∫(P·∇)E.sub.ext dV(5)

where the integral is to be taken over the volume V which includes thesample but not the sources of the field. For dielectrics with only P1,P2 and P3 contributions F_(z).sup.± ∝(ε-1), using Eq. (4). Since E_(ext)is proportional to the potential difference U between the electrodes,F_(z).sup.± ∝U². By contrast, P4 contributions cause the dielectric tobe either attracted to or repelled from the region of higher electricfield density, depending upon the sign of the surface charge andpolarity of the field. Contributions from P1, P2, P3 and P4 can beseparated by forming the linear combinations F⁺ +F⁻ and F⁺ -F⁻respectively: ##EQU5##

F.sub.Σ is used to give information about the dielectric constant ε.F.sub.Δ is used to calculate the surface charge density, and its signunambiguously determines the sign of the majority charge carriers at thesurface. In order to calculate the surface charge density, we place twodipole layers at both surfaces perpendicular to the z-direction of acrystal, assuming a cylindrical geometry for the sample, and neglect allcharges on the sides of the cylinder. Using the fact that E_(ext) onlydepends on the geometry F.sub.Δ is given by: ##EQU6## where D is thedipole layer thickness, 2a the diameter of the counter electrode (whichin this analysis is cylindrical), 2b the diameter of the sample, c thesample thickness, 2d the diameter of bias electrode which isdisc-shaped, L the length of cylindrical counter electrode, g thedistance from the sample surface to the bias electrode, N the number ofelectric charge carriers per unit area, e the electric charge of thecarriers and ε₀ the permittivity of vacuum. _(n) are the Besselfunctions of n-th order, where k_(0n) =x_(0n) /a, with x_(0n) being thesolutions of the zero order Bessel function ₀ (x_(On))=0. Taking intoaccount both the errors made by the approximations it is estimated thatthe calculated surface charge density should be correct to within oneorder of magnitude.

Because F⁺ and F⁻ are measured, and E_(ext) is also known (being appliedby the user), and the gradient of the electric field is known from thegeometry of the apparatus, the only remaining variable is ε, which cantherefore be calculated. If the geometry of the apparatus isstandardized, then the electric field gradient is a constant for eachmeasurement made, simplifying the calculations.

As mentioned above, P4 represents the contribution to polarization fromsurface charges, and can be determined from equation (7).

From equation (8), the surface charge density (N·e) is determined, sinceall of the other parameters are known.

Of particular interest to CDA are the cases where the charges consist ofdissociated charge carriers of finite mobility and a spatialdistribution within the sample which is initially non-uniform, due toeither frozen-in disequilibrium states or to the existence ofthermodynamically controlled surface/subsurface space charge layers.

In FIGS. 2A-2C there are shown schematically three cases of interestused here to illustrate the response of a dielectric material to annonhomogeneous electric field expressed as square root of the force(|F|)^(1/2) versus the applied bias voltage U. FIG. 2A represents anexample of an ideal dielectric in which an nonhomogeneous electric fieldgenerates a straight line passing through the origin with a slopeproportional to (ε-1)^(1/2). FIG. 2B represents a dielectric with adielectric constant Ξ=1 with q charge carriers of mobility μ[mu], andwith a positive surface charge with a positive bias voltage generatingat first a repulsion between sample and electrode, followed by anattraction which leads to a straight line not passing through theorigin. FIG. 2C represents the analogous case for a negative biasvoltage and the corresponding response of the sample characterized by anenhancement of the attractive force not passing through the origin. Thesimplified geometry depicted in FIGS. 2-2C is for the sake ofillustration only and may be modified according to the other possiblesample/electrode arrangements cited in this patent disclosure.

OPERATION

Measurement of the attractive and repulsive force due to the presence ofcharge carriers and possible non-uniform distribution of charge carriersunder negative and/or positive bias allows the derivation of informationabout the nature of the charges in the sample, about their sign,concentration, spatial distribution, mobility and relaxation times.Likewise, information can be derived about the dielectric constant, itsdependence on the various parameters, and about dipole or higher polerelaxation processes, though such information ma also be obtained byconventional impedance measurements in symmetrical condensorarrangements, e.g., without the special features of the CDA half cellarrangement which is described in this patent disclosure.

Referring now to FIGS. 4, 4A and 5, the apparatus shown therein siutilized int he following manner. A sample, such as a sample of olivine,obsidian, silica, or some other material, is configured and polished tohave a flat surface, such as sample 50 with surface 60. The sample isplaced upon a support 190, which may be simply a coil of the wire 130.The wire 130 is preferably of fused silica.

A D.C. power supply 200 is electrically connected t the windings 80, andis used to energize the windings so as to heat the furnace 40 andthereby heat the sample 50.

As noted above, the balance 10 is a conventional bottom-loading balance;however, it is modified in accordance with the present invention, suchas by the addition of circuitry and electrodes to form the capacitor 90.Reference to the balance 10 herein shall be to the balance as somodified.

As shown in FIGS. 1, 4 and 5, the sample 50 is attached to a wire 130 orother support mechanism, which is in turn supported by the hand-downwire 20. The balance 10 includes a balance arm 140, from a first end 150of which the wire 20 is attached, either directly as shown in FIG. 4 orby means of another attachment device such as a loop 160, as shown inFIG. 1.

The balance arm 140 has a second end 170. When the mass of a sample suchas sample 50 is altered, the balance 10 detects a variation in theposition of the end 170, such as by means of a photodiode array 135, ina standard manner. Other conventional position or motion detection meansmay be utilized, such as electrical or capacitive means. The balance 10includes a means 180 for restoring the second end 170 to its originalposition when the mass of a sample (such as sample 50) is altered.

In the present invention, the actual mass of the sample 50 is notaltered, but the apparent mass (i.e., the mass detected by the balance10) is altered, due to the attractive force established between thesample 50 and the electrode 30 upon heating of the sample 50 andestablishment of an electric field across the capacitor 90.

The furnace 40, the sample 50, the arm 140, the photodetector array 135,and the electrode 30 are preferably at least partially enclosed in achamber 210 with seals 220 and 230 and means 240 and 250 for injectingand releasing nitrogen, respectively. The injecting means may include asource 255 of pressurized nitrogen, or may be a pump or some other meansfor providing a nitrogen environment. The nitrogen (N₂) is utilized toprevent the sample from oxidizing, combusting, or otherwise undergoingchanges which may be undesirable. It will be appreciated that otherenvironments may be utilized that fulfill this function, such as heliumor other inert gases. Alternatively, oxygen, hydrogen, carbon monoxide,carbon dioxide, or other oxidizing or reducing gases may be utilized,depending upon the desired application, since these gases may result inbetter detection of peroxies.

A conventional thermostatic control 260 is provided at the furnace 50,and is coupled to a controller 270 via controller connector 280. At thecontroller 270, the operator of the apparatus may choose the desiredtemperature range, and set the thermostatic control 260 to maintain aparticular temperature. Typically, a sample will be tested at a varietyof temperatures in a given run.

Once the sample 50 has been heated to the desired, predeterminedtemperature, a voltage is supplied by means of the power supply 200 tothe electrode 30. The windings 80, which as indicated above act as acounterelectrode, are grounded, so that the total potential across thecapacitor 90 is due to the power supply 200.

Applicants have learned that the surface charges on many types ofminerals alter with both temperature and applied potential, and thatthis is an indication of the amount of peroxies, or impurities, withinthe sample. In the area of insulators or semiconductors, this providesan important method of detecting defects in the crystalline structure,such as in silica or silicon, since the defects may cause migration tothe surface or subsurface of the sample of charge carriers. Thus, ameasurement of the effect of applied temperature and external potentialupon the sample 50 provides a measurement of the amount of impuritieswithin the sample. Such effects are detected by measuring the apparentmass of the sample 50 by means of the balance 10.

As the sample 50 heats up, if peroxies or other impurities are present,they will migrate to the surface of the sample. This may result ineither an initial positive charge at the surface (such as in the case ofperoxies), or an initial negative charge. If the applied externalvoltage is positive and the surface/subsurface charge in the sample isalso positive, there will be an electrostatic repulsion between theelectrode 30 and the sample 50. However, as the potential is continuallyapplied by the electrode 30, eventually there is a reorientation of thedipoles within the sample 50, with the result that there is anultimately attractive force between the electrode 30 and the sample 50.

Both the attraction and the repulsion are reflected by the balance 10,because each results in an alteration in the position of the end 160 ofthe arm 140. The photodetector array 135 detects the change in positionof the end 160, and the restoring means 180 restores the arm 140 to itsinitial position. The amount of force (or, alternatively, work)necessary to perform this restoring function is determined in aconventional fashion by an analyzer 290 which is coupled to both thearray 135 and the restoring means 180, for reading the responses of thearray 135 and for controlling the means 180. The analyzer has an outputwhich is a correlation of the applied voltage with the restorativeforces necessary to rebalance the arm 140, and thus the analyzer outputreflects the amount of subsurface charges present in the sample 50.

The analyzer output is recorded by a conventional means for recording300, which may be include a graph generator, an electronic memory, andother means of storing and displaying information.

Typical results of the recorder 300 are as shown in FIGS. 2A-2C,discussed above. Additional results are shown in FIGS. 7-13, all ofwhich relate to actual tests utilizing the method and apparatus of thepresent invention on obsidian. FIG. 7 represents the effective massdetected by the balance when obsidian has been heated to the varioustemperatures shown, and then an external voltage of 75 volts is applied.As indicated by that figure, at first when the voltage is applied, thereis an initial attraction of the sample to the bias electrode (indicatedby the rise in the effective mass, or delta-m), and then over time (notethe 1-minute scale on the right), the attraction increases. Thisindicates attraction due to peroxies in the sample, and thus provides ameasure of the amount of these peroxies. Note that as the temperatureincreases, the effect of the peroxies on the effective mass alsoincreases.

FIG. 8 shows the effect on a sample wherein there is initially arepulsion, which is due to the presence of positive subsurface charges.Past a certain applied voltage for each given temperature, the orienteddipoles cause electrostatic attraction with the bias electrode, and thusthere is eventually a net attraction despite the presence of theperoxies causing a positive subsurface charge. The amount of the initialrepulsive effect is a measure of the amount of peroxies. In the case ofquality control for silica or other semiconductor products, this wouldbe a measure of the amount of impurities within the product.

FIG. 9 shows, in the dotted-line graph, the response of a sample whichhas been treated by heating it up to a high temperature, such as between300° and 700° C., and then rapidly cooling it, thereby "freezing in" thesubsurface charges due to the peroxies. The solid-line portion of FIG. 9shows the response of a sample where the subsurface charges have notbeen frozen in.

FIGS. 10 and 11 show the results of the method and apparatus of theinvention wherein positive and negative external biasing potentials,respectively, are applied to a sample of obsidian wherein the subsurfacecharges have been frozen in, as described above.

FIG. 12 shows a set of test results for obsidian at various appliedvoltages and again indicates the attraction due to the peroxies. Theinset of FIG. 12 is an enlarged section near the origin of the graph.The results shown in FIG. 12 are analogous to those of FIG. 8, exceptthat they reflect the use of a negative, instead of positive, appliedpotential.

FIG. 13 shows the results of a test at room temperature for a sample ofobsidian wherein the peroxy subsurface charges have been frozen in asdescribed above. As indicated, past a certain voltage (here, about 275V. applied external potential), there is a discharge between the sampleand the windings of the furnace, i.e. the counterelectrode.

An alternative embodiment of the apparatus of the invention is shown inFIG. 6. In this embodiment, the sample 50 is heated by infraredradiation, rather than by convection and/or conduction heating, as withthe first embodiment. A combination of these methods of heating thesample may also be utilized. In the embodiment of FIG. 6, a biaselectrode 310 and a counterelectrode 320 are used, and the sample 50 ispositioned therebetween, as with the embodiments of FIGS. 1, 4 and 5.However, in this embodiment, the counterelectrode 320 does not serve asa heater, and thus the configuration may be one of many differentshapes, allowing for great latitude in determining the geometricconfiguration of the resulting capacitor 330. In FIG. 6, thecounterelectrode 320 is chosen to be larger than the electrode 310, toensure that the resulting electric field 340 is nonhomogeneous.

Infrared generators 350 and 360 are provided, and heat the sample 50 byradiative heating. Infrared reflectors 370 and 380 are provided,positioned near the generators 350 and 360, to maximize theeffectiveness of the infrared generators.

The following variations may be made on the method and apparatus of theinvention. The electrodes and the sample may be configured such that asignificant portion of the electric field lines emanating from the biaselectrode traverse the sample, and such that the average distancebetween the surface of the sample opposing the bias electrode and thegrounded equipotential surface, called the counter gap, is larger thanthe gap between the bias electrode and the sample. The gap and thecounter gap may be of various relative sizes.

In another embodiment, the bias electrode, instead of being of planarshape, may instead be of a generally nonplanar shape including but notlimited to a wedge-like or needle-like shape or a 1-dimensional or2-dimensional array of needle-like electrodes, each electricallyinsulated from all other electrodes with the provision to apply a biasvoltage to each of them individually.

It is advantageous to minimize the linkage force between the biaselectrode and the means for applying a potential thereto.

In one embodiment, the electrodes and the sample may be verticallyoriented adjacent one another. In this and the other embodiments, gridmay be inserted in the gap to be operated as a control electrode.

In another embodiment, a mechanical device is included which allows,when operated, to mechanically touch the sample in order to ground it orto charge it to a preselected positive or negative potential.

In another embodiment, radioactive source is included which allows, whenbrought into proximity of the sample, the electrical discharge of thesample by ionization.

In another embodiment, a cooling device is included which allows, whenoperated, to control the temperature of the sample to temperatures belowambient. The cooling device may be used in place of or in conjunctionwith the furnace.

In another embodiment, device may be added to expose the sample toelectromagnetic radiation or electron or other particle bombardment.

The apparatus as discussed above is preferably contained in a gas-tightor vacuum-tight container.

In an alternative embodiment, secondary electrode may be added to thebias electrode to monitor the rise and fall of the bias. The biaspotential may be increased or decreased or reversed in a step-wise timefunction, or in an oscillatory fashion.

In the above description, the forces F_(z).sup.± were measured with abalance as a force measuring device, and the direction z was chosen tocoincide with the direction of the gravitational vector g. However, thecoincidence between the z and g vectors may introduce complications whenthe samples under study lose or gain mass during measurement. In suchcases, the baseline under zero field shifts according to the rate ofmass loss or gain. This introduces measuring errors. Applicants have nowdetermined that the actual task of CDA, namely the measurement ofsurface charge layers and of the distribution of mobile charge carriersand their sign, can be performed without knowledge or measurement ofconcomitant mass gains or losses.

A substantial improvement of the technique was achieved by using as aforce measuring device a vertical pendulum. With such an arrangement,the force F_(z).sup.± which responds to changes in mass of the sample isdirected parallel to the axis of the pendulum z which in turn is set upto be parallel to the gravitational vector g. Hence, under static ornear-static conditions, the apparatus is indifferent to changes of theforce F_(z).sup.±. On the other hand, two orthogonal directions remainin x and y which can be exploited to measure forces F_(x),y.sup.± thatare caused by the response of the sample to externally applied fields.

This introduces the possibility to combine measurements according to theabove-described charge distribution analysis or CDA (which are carriedout in an electric field gradient) with other measurements such as thoseof the magnetic susceptibility (which are carried out in a magneticfield gradient). If, for instance, an electric field gradient is set upalong the x axis, a force F_(x).sup.± will be generated in dielectricmaterial which provides information about the dielectric constant ofsaid material. If a magnetic field gradient is set up along the y axis,a force F_(y).sup.± will be generated which provides information aboutthe magnetic susceptibility of the same material.

FIGS. 14-17 show embodiments in which a sample 500 is supported on aplatform 510, which is carried by a vertically-disposed support beam 520mounted at 530 at an anchor point 530. The sample 510 is positionedrelative to a bias electrode and a counter electrode as in the previousembodiments, such as FIGS. 4, 4A, 5 and 6, though these are notseparately shown in FIGS. 14-17. The deflection detection system in eachof FIGS. 14-17 is designated as 540.

FIGS. 14-17 show different possible configurations for the sample andplatform, the anchor of the vertical pendulum, and the deflectiondetection system. In each configuration, as described above, changes inmass do not affect determination of the surface charges and othermeasurements and calculations made using the present invention.

In FIGS. 14 and 15, the sample 500 is carried at the bottom of thependulum or beam 520. In FIG. 14, the anchor 530 is somewhere along themiddle of the beam 520 (most conveniently at the center), and the system540 is at or near the top of the beam. In FIG. 15, the positions of theanchor and deflection detection system are reversed relative to FIG. 14.In both FIGS. 14 and 15, the sample is carried below the center ofgravity of the beam-plus-sample system.

In FIGS. 16 and 17, the sample 500 is carried at the top of the beam520. In FIG. 16, the anchor 530 is again at the center of the beam, orsomewhere else along its length, while the system 540 is at or near thebase of the beam 520. In FIG. 17, the positions of the anchor and thedeflection detection system are reversed relative to their positions inFIG. 16. In both FIGS. 16 and 17, the sample is carried above the centerof gravity of the beam-plus-sample system.

The configurations of FIGS. 16 and 17 have the distinct advantage that,not only is the effect of gravity compensated for by the verticalarrangement, but also, the sample platform 510 is easily accessiblebecause of its placement on top of the support beam 520. FIG. 18 showsan embodiment corresponding to the configuration of FIG. 17, includingan aluminum block 550, a position control and deflection detectiondevice 560, and a support or anchor 570. The support 570 in thepreferred embodiment includes a metal 580 with a low melting point, suchas mercury or Wood's metal (which is an alloy including tin). A heatingblock 590 having heaters 600 is provided to keep the metal 580 in aliquid state, and is insulated from the table and the aluminum block 550by thermal insulators 610 and 620, respectively.

The beam or rod 520 is positioned within a bore 630 in the block 550,and is thus in a metastable position. For minimizing the mass of thebeam 520 in the embodiment of FIG. 18, the beam may be a hollow tubeclosed at its lower end. For instance, the beam 520 may be a thin-walled(4 mm) fused silica tube such as an EPR or NMR tube.

A sample support 640 is carried on top of the beam 520, and a sample 500is placed on the support. When force is exerted on the sample asdescribed above with respect to the earlier embodiments, the system 560maintains the beam 520 in a vertical position, and the forces necessaryto do so are utilized in the calculations described previously.

It will be understood that the embodiments described herein are merelyillustrative, as there are many variations and modifications which maybe made by those skilled in the art. Thus, the invention is to beconstrued as being limited only by the spirit and scope of the claims.

We claim:
 1. A method for measuring a static dielectric constant of amaterial, including the steps of:(1) placing a sample of the material ona force-measuring device; (2) applying a nonhomogeneous electric fieldto a volume including the sample; (3) measuring a force upon the sampleas a function of the applied electric field; and (4) deriving a valuefor the static dielectric constant of the material from the measuredforce.
 2. A method for measuring a static dielectric constant of amaterial, including the steps of:(1) placing a sample of the material ona force-measuring device; (2) applying a nonhomogeneous electric fieldto a volume including the sample; (3) measuring a force upon the sampleas a function of the applied electric field; and (4) deriving a valuefor the static dielectric constant of the material from the measuredforce by determining a slope of a curve of the square root of themeasured force as a function of the applied voltage.
 3. The method ofclaim 1, wherein step 3 is carried out by applying a potential across acapacitor which includes a dielectric.
 4. The method of claim 1,including, before step 2, the step of adjusting the force to apredetermined setting, and wherein step 4 is carried out by readjustingthe force-measuring device of the predetermined setting, and determiningan amount of potential change across the capacitor required for suchreadjustment.
 5. A method for measuring a static dielectric constant ofa material, including the steps of:(1) placing a sample of the materialon a force-measuring device; (2) applying a nonhomogeneous electricfield to a volume including the sample; (3) measuring a force upon thesample as a function of the applied electric field; and (4) deriving avalue for the static dielectric constant of the material from themeasured force, wherein the steps 2 and 3 are both carried out for atleast two electric fields of opposite polarity, such that a plurality offorces ar measured, and step 4 includes the step of comparing theplurality of forces for invariance under change in polarity.
 6. Themethod of claim 5, wherein step 3 is carried out by applying a potentialacross electrodes of a capacitor, and the electric fields are generatedby applying positive and negative potentials across the electrodes.